Two different configurations each use three identical point masses of connected by light

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics

Problem

Two different configurations each use three identical point masses of 0.50 kg0.50\,\text{kg} connected by light, rigid rods that can be re-arranged quickly on a smooth tabletop. • Arrangement A: the masses are located at (+0.25 m,0)(+0.25\,\text{m},0), (−0.25 m,0)(-0.25\,\text{m},0), and (0,+0.25 m)(0,+0.25\,\text{m}). • Arrangement B: the masses are located at (+0.25 m,0)(+0.25\,\text{m},0), (0,+0.25 m)(0,+0.25\,\text{m}), and (0,−0.25 m)(0,-0.25\,\text{m}). In both arrangements a vertical axis passes through the origin and is perpendicular to the tabletop. (a) Calculate the rotational inertia of Arrangement A about the stated axis. Show your work. (b) Calculate the rotational inertia of Arrangement B about the same axis. (c) Determine the percent difference between the two rotational inertias you found. State which arrangement is more resistant to being set into rotation and explain why. (d) In Arrangement B, the mass initially at (0,−0.25 m)(0,-0.25\,\text{m}) is slid along the yy-axis to (0,−0.15 m)(0,-0.15\,\text{m}) while the other two masses remain fixed. Compute the new rotational inertia and state the change compared to the original value for Arrangement B.

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